Pete wants to use a one sample ttest to test the mean of the average lifetime of light bulbs of a particular type, but he does not know if the observations are normally distributed. To test this, he applies Shapiro and Wilk's Wtest to the sample of data.
His observed data:

bulb1

bulb2

bulb3

bulb4

bulb5

bulb6

bulb7

bulb8

bulb9

bulb10

lifetime(hrs)

355.0

359.5

379.3

366.5

325.1

334.4

308.4

355.6

381.2

316.9


bulb11

bulb12

bulb13

bulb14

bulb15

bulb16

bulb17

bulb18

bulb19

bulb20

lifetime(hrs)

379.0

338.7

380.3

366.4

368.1

333.3

390.7

337.4

373.3

370.0



Determine the null hypothesis:

Null hypothesis: The data is normally distributed

Collect the data:
>

$X\u2254\left[355.0\,359.5\,379.3\,366.5\,325.1\,334.4\,308.4\,355.6\,381.2\,316.9\,379.0\,338.7\,380.3\,366.4\,368.1\,333.3\,390.7\,337.4\,373.3\,370.0\right]\:$

Run the Shapiro Wilk wTest:
>

$\mathrm{Student}:\mathrm{Statistics}:\mathrm{ShapiroWilkWTest}\left(X\right)\:$

Shapiro and Wilk's WTest for Normality

Null Hypothesis:
Sample drawn from a population that follows a normal distribution
Alt. Hypothesis:
Sample drawn from population that does not follow a normal distribution
Sample Size: 20
Computed Statistic: .935508635130523
Computed pvalue: .207505438819378
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.
 
The Shapiro and Wilk's Wtest returns a pvalue = 0.207505. From this pvalue, Pete concludes that the data can indeed be assumed to be normal and proceed with one sample ttest.